Representations of B^a(E)

We present a short and elegant proof of the complete theory of strict representations of the algebra B^a(E) of all adjointable operators on a Hilbert B-module E by operators on a Hilbert C-module F. Aanalogue for W*-modules and normal representations is also proved. As an application we furnish a new proof of Blecher's Eilenberg-Watts theorem.Comment: Publication data added, corrected an ambiguity in the formulation of Corollary 1.20 (present also in the published version) and adjusted the proof appropriatel

Effects of fungicides and bactericides on orchid seed germination and shoot tip cultures in vitro

Amphotericin B, benomyl, gentamycin, nystatin, quintozene penicillin G, sodium omadine, and vancomycin singly and in several combinations have no deleterious effects on the germination of orchid seeds, but inhibit the growth in vitro of shoot tip explants. © 1981 Martinus Nijhoff/Dr W. Junk Publishers

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd

The Botryosphaeriaceae: genera and species known from culture

In this paper we give an account of the genera and species in the Botryosphaeriaceae. We consider morphological characters alone as inadequate to define genera or identify species, given the confusion it has repeatedly introduced in the past, their variation during development, and inevitable overlap as representation grows. Thus it seems likely that all of the older taxa linked to the Botryosphaeriaceae, and for which cultures or DNA sequence data are not available, cannot be linked to the species in this family that are known from culture. Such older taxa will have to be disregarded for future use unless they are epitypified. We therefore focus this paper on the 17 genera that can now be recognised phylogenetically, which concentrates on the species that are presently known from culture. Included is a historical overview of the family, the morphological features that define the genera and species and detailed descriptions of the 17 genera and 110 species. Keys to the genera and species are also provided. Phylogenetic relationships of the genera are given in a multi-locus tree based on combined SSU, ITS, LSU, EF1-α and β-tubulin sequences. The morphological descriptions are supplemented by phylogenetic trees (ITS alone or ITS + EF1-α) for the species in each genus.We would like to thank the curators of the numerous fungaria and Biological Resource Centres cited in this paper, for making specimens and cultures available for examination over the past 15 yr, without which this study would not have been possible. Part of this work was supported by Fundação para a Ciência e a Tecnologia (Portugal) through grant PEst-OE/BIA/UI0457/2011. Artur Alves and Alan Phillips were supported by the programme Ciência 2008, co-funded by the Human Potential Operational Programme (National Strategic Reference Framework 2007–2013) and the European Social Fund (EU).publishe